Polinômios para os ajustes das trajetórias médias e das funções de covariâncias do crescimento de tourinhos testados em provas de ganho em peso

Abstract

Data were collected from body weights of 3,356, 843 and 884 young bulls of the genetic groups Nellore, Canchim (5/8 Charolais + 3/8 Nellore) and MA (21/32 Charolais + 11/32 Nellore), respectively. The database of Nellore comprised data from 37 performance tests performed by the group Provados a Pasto, in the State of Goiás, between the years of 1997 and 2009. Data from Canchim and MA bulls refers to ten performance tests, performed between the years of 1997 and 2007, except 1999, belonging to the program of evaluation of bulls in the farms of Agropecuária Ipameri, in the State of Goiás. The growth trajectories were adjusted by ordinary and Legendre polynomials (linear up to quintic) and quadratic B-splines (with two to four equidistant intervals). The comparisons between the different models were performed by the coefficient of determination (R2), mean absolute deviation (MAD), mean square residual (MSR), value of restricted likelihood function (-2RLL), Akaike information criterion (AIC) and Consistent Akaike (CAIC). For genetic groups Nellore and MA, the polynomial B-spline with four intervals was the model that provided the best fit. For Canchim, the polynomial B-spline with three intervals was adequate to model the growth trajectory. After identifying the best model for the growth trajectory, the minimum number of age classes to model the weight of the residual variance in genetic evaluation of young bulls MA were evaluated. The numerator relationship matrix of the group consisted of 1,491 animals. The mean trajectory (polynomial B-spline of quadratic order with four equidistant intervals), nested in the year of performance test, and contemporary group effect were considered in the statistical models. Contemporary groups were defined by the variables age and years of birth and date of weighing. As random effects were considered additive genetic and permanent environmental (both modeled with polynomial B-spline of order quadratic with four intervals). The number of classes to model the residual variance were one, two, four, eight and 16. After analyzing the model with 16 classes, adjacent classes of residual variances were grouped, giving rise to models with 14, 13, 10 and nine classes. Variance components were estimated by restricted maximum likelihood (REML). The values of -2RLL, the AIC and CAIC allowed to select the structure of the best fit of residual variance. For modeling the residual variance, the model with nine age classes were the more appropriate. In the third and final step, B-spline models with one, two, three and four intervals to fit additive genetic and permanent environmental random effects were compared, to define the number of intervals for the adjustment of covariance functions. The less parameterized model, which used the covariance function with a quadratic polynomial B-spline with one interval describing the variability of random effects were evaluated as the most appropriate.